An interface-regularizing model for compressible three-fluid flows with interfacial tensions. (English) Zbl 1521.76496
Summary: We present a diffuse-interface model for simulating compressible three-fluid flows with surface tension. In this model different fluids are separated with resolved interfaces. We first deduce the jump conditions across the material interfaces under surface tension. The interfaces are represented with the advection equations for volume fractions. Traditional methods for solving these equations result in serious numerical smearing of interface surfaces. To minimize this numerical effect, we introduce mathematical regularization of the governing equations by implementing an artificial compression method. The mathematical regularization is introduced in such a way that the jump conditions across the material interface maintain unaltered. Further we demonstrate that for the three-fluid formulation the direct implementation of the artificial compression method for each volume fraction can violate the non-negativity constraints for volume fractions. To cope with this problem, we propose a simple and robust method to ensure the volume fraction constraints. In this method instead of the original advection equations for volume fractions, we solve the advection equation with an additional compression term for new characteristic functions in the form of non-linear combinations of volume fractions. Moreover, a HLLC solver for solving the model equations is developed. The numerical results of several benchmark problems display the efficiency of the proposed algorithm.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 68U07 | Computer science aspects of computer-aided design |
| 76Nxx | Compressible fluids and gas dynamics |
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